The current invention relates to a method and a device for determining an angle of rotation or a path.
In various applications, particularly in devices intended to aid in determining the angular position of a rotatable shaft, it is desirable to know the precise angular position of the shaft. This requirement can be fulfilled, for example, with the aid of analog angle sensors, for example potentiometers, which after being turned on, immediately output the current angular position value in the form of a voltage in every position.
If devices of this kind are used for angular measurement of angular ranges greater than 360xc2x0, the problem arises that it is no longer possible to determine which rotation the shaft is currently in. In order to evaluate angular ranges that are greater than 360xc2x0, however, incremental measuring transmitters can be used, in which the angular position is determined through forward and backward counting of pulses.
Such incremental measuring transmitters, however, cannot execute absolute angle measurement because it is only possible to count increments that have passed by a receiver.
In some technical measuring tasks, the use of incremental measuring transmitters generates phase measurement values; the values that are actually to be measured, such as an angle, a path, or a distance, must be determined from these phase measurement values. In order to increase the range of unambiguity (corresponding to a phase range from 0-2xcfx80) it is possible to use at least one other measurement conduit with a different phase slope and to derive a greater unambiguity range from a suitable combination of measurement values.
Examples of this include distance measurement using RADAR or modulated laser light. In these instances, N measurements are executed at different frequencies f1, . . . fN. At the reception point, the signals reflected from a target at a distance x have the following phase shifts (c=the speed of light):       α    i    =            2      ·      π      ·              f        i            ·      2      ·      x        c  
The phase shifts are thus proportional to the value that is to be measured and proportional to the frequency used. However, the actual measurement values of the phases always lie in the range from 0 to 2xcfx80, i.e. are always determined, with the sole exception of integral multiples of 2xcfx80.
Another example that should be mentioned is an optical angular sensor. In this case, a scan of N optical line gratings is executed, where N tracks with optical line gratings are placed on a disk or a cylinder. There are ni periods or lines in one rotation. If the phase positions of the tracks are measured in relation to a fixed measurement window with the aid of optoelectronic detectors, this yields the following phase lengths:
xcex1i=(nixc2x7xcfx86) modulo (2xcfx80).
The phases are thus proportional to the rotation angle xcfx86 and the periodicities. Here, too, the actual measurement values of the phases always lie in the range from 0 to 2xcfx80.
Finally, multiple wave interferometry should also be mentioned. Here, too, for example paths x are measured through the use of at least two different light wavelengths xcexi, which yields an increased unambiguity range of   Λ  =                              λ          2                ·                  λ          1                                      λ          2                -                  λ          1                      .  
Here, too, an appropriate dimensioning yields a phase path of the kind indicated above.
The evaluation of the signals obtained with methods of this kind, i.e. the determination of x and xcfx86, is carried out using vernier methods.
In the classic vernier method, the difference is calculated between two phase signals, where for the case in which this difference is less than zero, 2xcfx80 is added. This method has significant limitations since measurement errors in the phases have full impact on the end result. Furthermore, a method of this kind functions only if the two periodicities under consideration differ by precisely 1.
DE-OS 195 06 938 has disclosed a modified vernier method in which the value of a variable to be measured is determined from two phase signals through weighted addition and through the further addition of an angle range-dependent constant. This method excels in its capacity for significantly reducing measurement errors in the phase signals. For this method, too, however, it is necessary that the two periodicities under consideration differ by precisely 1.
Finally, DE-P 1004260 has disclosed a method for determining a rotation angle or distance through the evaluation of phase measurement values. In this method, the phase values that are measured in an N-dimensional space are mapped as Nxe2x88x921 new signals Si by means of a linear transformation A. These signals Si are transformed with the aid of a quantizing mechanism into corresponding integral values Wi and are converted by means of a linear mapping C into N real values Zi. Weighted phase measurement values xcex1i modulo 2xcfx80 are added to these values, yielding N estimates for the angle xcfx80 to be measured. The N estimates are corrected if need be at their discontinuity points and are added up in a weighted fashion taking their phase angles into account.
The object of the invention is to supply, through the simplest means possible, measurement values for distances x and angles xcfx86 on the basis of at least two phase measurement values. It should as a result no longer be necessary to abide by the requirement in the conventional method that the two periodicities must differ by precisely 1.
The invention provides for a particularly simple method, which can reliably determine measurement values that are to be determined, e.g. an angle xcfx86 or a path or distance x. By contrast with conventional methods, there is a large degree of freedom in the selection of periodicities for the determination of at least two phase signals. The weighting of the individual measurement values or estimates in the manner that is provided according to the invention has turned out to be particularly easy to execute, computationally speaking.
According to a first embodiment of the method according to the invention, for the case in which two phase values xcex11, xcex12 are supplied, the working value k, which is used in the process of determining a rotation angle or a path, is calculated by rounding the term:       [                                        α            1                    ·                      n            2                          -                              α            2                    ·                      n            1                                      2        ·        π              ]    .
In this case, two phase values xcex11, xcex12 are evaluated, which are respectively obtained from sensors or measuring transmitters that each have n1 and n2 periods. Computationally speaking, it is easy to carry out the generation and use of such a working value based on two phase values. In this instance, the rounding is the replacement of the calculated value with the nearest smaller or larger whole number. The deviation of the calculated term from the nearest whole number is a measure of the achievable precision of the method.
A scaling relation between the periodicities n1, n2 is suitably selected to be an equation with the form
k2xc2x7n1xe2x88x92k1xc2x7n2=1
Of the infinite number of solution pairs k1, k2, the one with the smallest numerical values is advantageously used.
According to a particularly preferable embodiment of the method according to the invention, the at least two scaled estimates are calculated in the form                     Φ        ⁢                  xe2x80x83                ⁢                  s          i                            2        ·        π              =                                        α            i                                2            ·            π                          +                  k          ·                      k            i                                      n        i              ,
where i=1, 2 . . . N, and k=the working value.
It is also preferable that the weighted summation of the at least two scaled estimates for obtaining a determined estimate "PHgr"meas be carried out in the form             Φ      meas              2      ·      π        =            ∑              i        =        1            N        ⁢                  [                                            Φ              ⁢                              xe2x80x83                            ⁢                              s                i                                                    2              ·              π                                ·                      g            i                          ]                    mod        ⁡                  (          1          )                    
where the gi ""s (i=1, 2 . . . N) represent the weighting factors for which xcexa3gi=1.
The calculated sum must be taken as modulo 1 (i.e. only the number of decimals need be taken into consideration). It turns out that the resulting estimate "PHgr"meas for the angle "PHgr" to be measured can be produced in a very precise and reliable fashion.
In the case of two phase measurement values, it is suitable to set the weighting factors g1, g2 each equal to 0.5. This setting turns out to be sufficiently precise for a large number of uses.
According to another preferred embodiment of the method according to the invention, an improvement in the precision of the estimate "PHgr"meas with similarly probable additive measurement errors in xcex11 and xcex12 is achieved if the weighting factors are produced in the form:       g    i    =                    n        i        2                              ∑          1          N                ⁢                  n          i          2                      .  
This weighting is optimal for the purpose of a minimal square of error. This weighting turns out to be very suitable particularly for systems with more than two phase signals to be evaluated, i.e. for N greater than 2.
According to another preferred embodiment, the weighting factors are produced in the form             g      i      xe2x80x2        =                                                      n              i                        ·                          w              i                                            2            q                          ⁢                  xe2x80x83                ⁢        with        ⁢                  xe2x80x83                ⁢                              ∑                          i              =              1                        N                    ⁢                                    w              i                        ⁢                          n              i                                          =              2        q              ,
where the wi""s represent whole numbers and are selected in such a way that the weights gxe2x80x2i come as close as possible to the ideal weight gi. The natural number q here determines the achievable precision. This selection of the weighting factors turns out to be particularly easy to execute in terms of computation since in the generation of this kind of weighting factors, the division by the term       ∑    1    N    ⁢      n    i    2  
or the multiplication by the reciprocal value of this term is eliminated. Only a division by the power of two 2q is required here, which in a two""s complement depiction, can be achieved computationally through a simple digit shift by q places to the right. The summation is suitably calculated with q bits, without regard to subtotal arithmetic overflows.
Preferred embodiments of the invention will now be explained in detail in conjunction with the accompanying drawings.